Transcript Number Strategy 1

Ministry of Education
Secondary Numeracy Project
Algebra in Multiplication
Kevin Hannah
Central Auckland Airport Hotel
23-24 February 2005
Algebra in Multiplication
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Computing using the distributive law
Recognising structure in numbers
Exploring algebraic expressions
What’s the answer?
7 x 98
How did you do it?
7 x 98 = 7 x 100 - 7 x 2
What’s the answer?
597 x 5
How did you do it?
597 x 5 = 600 x 5 - 3 x 5
What’s the answer?
407 x 8
How did you do it?
407 x 8 = 400 x 8 + 7 x 8
Are these correct?
7 x 98 = 7 x 100 - 7 x 2
915 x 8 = 900 x 8 + 15 x 8
597 x 11 = 600 x 11 - 3 x 7
3x(400-8) = 3x400 - 3x8
Are these correct?
8 x 300 - 7 x 8 = 8 x 293
80 x 7 - 5 x 7 = 85 x 7
79 x 11 = 70 x 11 +9x9
12x40 - 8x12= 8x(40-12)
What’s missing?
6 x 600 + 7 x 6 = 6 x 607
80 x 6 - 6 x 6 = 74 x 6
58 x 13 = 50 x 13 + 8 x 13
5x(70-2) =5x70 - 5x 12
Fill in the gaps
6 ( m + 7) = 6m + 42
8c - 48 = 8(c - 6)
7 ( m + 9 ) = 7m + 63
5(y-2) =5y - 10
Expand
5 ( y + 6) = 5y + 30
7(x - 10) = 7x - 70
4 ( 2m + 3 ) = 8m + 12
6(3r-9) = 18r - 54
Factorise
3 ( n + 2) = 3n + 6
8(x - 4) = 8x - 32
5 ( 4p + 3 ) = 12p + 15
7(6 - 5y) = 42 - 35y
Recognising Structure
a(b ± c) = ab ± ac